To be able to produce ever finer structures with lithographic methods in the production of semiconductor components, light of an increasingly shorter wavelength is used. When working in the extreme ultraviolet (EUV) wavelength range, for example, at wavelengths between about 5 nm and 20 nm, it is no longer possible to work with lens-like elements in the transmission mode, rather illumination and projection objectives of mirror elements are constructed, having reflective coatings adapted to each working wavelength. When using working wavelengths in the ultraviolet (UV) wavelength range, e.g. at 248 nm, 193 nm or 157 nm, reflective optical elements can also be used. At UV wavelengths optical elements are primarily used that work in the transmission mode. The optical elements usually have a substrate which, on a first surface, has a functional coating that serves to optimize the reflectivity or transmission of the desired working wavelength on the optical element.